Monday, July 22, 2024
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Quantitative Aptitude: Boats and Streams Set 1

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  1. Vimal can row a certain distance downstream in 14 hoursand return the same distance in 21 hours. If the speed of the stream is 6 kmph, Find the speed of Vimal in the still water?
    A) 21 kmph
    B) 15 kmph
    C) 30 kmph
    D) 35 kmph
    E) None of these
    View Answer
    Option C
    Solution:
    Speed of Vimal in still water = x
    Downstream Speed = (x + 6)
    Upstream Speed = (x – 6)
    Downstream Distance = Upstream Distance
    14(x + 6) = 21(x – 6)
    2x + 12 = 3x – 18
    x = 30 kmph.
  2. Rahul can row a certain distance downstream in 12 hour and return the same distance in 18 hour. If the speed of Rahul in still water is 12 kmph, find the speed of the stream?
    A) 2.1 kmph
    B) 1.5 kmph
    C) 4.4 kmph
    D) 2.4 kmph
    E) None of these
    View Answer
    Option D
    Solution:
    Let the speed of the stream be x kmph
    Down stream = (12+x)
    Up stream = (12−x)
    suppose the distance traveled be y
    y/(12+x) = 12 —(1)
    y/(12−x)= 18 —-(2)
    From eqn (1) and (2)
    x= 2.4 kmph
  3. Anil can row 18 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream?
    A) 5 kmph
    B) 6 kmph
    C) 4 kmph
    D) 3 kmph
    E) None of these
    View Answer
    Option B
    Solution:
    Stream Speed = a kmph
    Time Taken = x km
    Downstream speed = (18 + a) kmph
    Upstream speed = (18 – a) kmph
    Time taken to travel downstream = 2 * Time taken to travel upstream
    (18 + a) / x = 2(18 + a) / x
    18 + a = 36 – 2a
    3a = 18
    a = 6 kmph
    OR USE FORMULA
    Speed of boat = [tu+td]/[tu-td] * Speed of stream
    So 18 = [2x + x]/[2x – x] * Speed of stream
  4. Mr. Suresh can row to a place 48 km away and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is?
    A) 1 kmph
    B) 3 kmph
    C) 4 kmph
    D) 6 kmph
    E) None of these
    View Answer
    Option A
    Solution:
    Downstream speed = 4/x kmph
    upstream speed = 3/x kmph
    48/(4/x) + 48/(3/x) = 14
    Solving we get x = 1/2 kmph
    So, Speed of downstream = 8 kmph, Speed of upstream = 6 kmph
    Stream Speed = 1/2(8 – 6) kmph = 1 kmph
  5. Mr.Ramesh’s speed with the current is 20 kmph and the speed of the current is 5 kmph. Ramesh’s speed against the current is?
    A) 15 kmph
    B) 19 kmph
    C) 17 kmph
    D) 10 kmph
    E) None of these
    View Answer
    Option D
    Solution:
    Ramesh’s speed with the current = 20 kmph
    => Ramesh’s speed + speed of the current = 20 kmph
    Speed of the current = 5 kmph
    Speed of Ramesh = 20 – 5 = 15 kmph
    Ramesh’s speed against the current = speed of Ramesh – speed of the current = 15 – 5 = 10 kmph
  6. Ravi can row 12 kmph in still water when the river is running at 6 kmph it takes him 1 hour to row to a place and to come back. How far is the place?
    A) 5.5 km
    B) 4.5 km
    C) 8.2 km
    D) 4.2 km
    E) None of these
    View Answer
    Option B
    Solution:
    Downstream Speed = 18 kmph
    Upstream Speed = 6 kmph
    Distance = x
    x/18 + x/6 = 1
    18x + 6x = 108
    24x = 108
    x = 4.5 km
    OR USE FORMULA:
    Distance = time [B2 – R2]/2*B
    So distance = 1 * [122 – 62]/2*12
    Distance = 108/24 = 4.5 km
  7. The different between downstream speed and upstream speed is 2 kmph and the total time taken during upstream and downstream is 2 hours. What is the upstream speed, if the downstream and upstream distance are 2 km each?
    A) 5.2 kmph
    B) 3.7 kmph
    C) 2.8 kmph
    D) 1.4 kmph
    E) None of these
    View Answer
    Option D
    Solution:
    2/x + 2/(x+2) = 2.
    x2 – 2 = 0
    x = 1.414kmph
  8. Rani can row 8 kmph in still water. If the river is running at 4 kmph it takes 90 minutes to row to a place and back. How far is the place?
    A) 4.5 km
    B) 8.2 km
    C) 4.2 km
    D) 3.5 km
    E) None of these
    View Answer
    Option A
    Solution:
    Speed in still water = 8 kmph
    Speed of the stream = 4 kmph
    Upstream Speed = (8-4) = 4 kmph
    Downstream Speed = (8+4) = 12 kmph
    Total time = 90 minutes = 90/60 = 3/2 hrs
    Let x is the distance
    x/12 + x/4 = 3/2
    x = 4.5 km
  9. Sumi can swim 6 kmph in still water. If the velocity of the stream be 2 kmph, the time taken by her to swim to a place 24 km upstream and back, is?
    A) 6 hours
    B) 5 hours
    C) 4 hours
    D) 8 hours
    E) 9 hours
    View Answer
    Option E
    Solution:
    Upstream speed = speed of man – speed of stream=6 – 2 = 4
    Downstream speed = speed of man + speed of stream=6 + 2=8
    Time taken to go upstream = distance/speed = 24/4 =6 hour
    Time taken to go downstream = distance/speed =24/8 = 3 hour
    Total time =6+3 = 9 hour
  10. Raghu can row 96 km downstream in 8 hours. If the speed of the current is 3 kmph, then find in what time will be able to cover 12 km upstream?
    A) 6 hours
    B) 5 hours
    C) 4 hours
    D) 8 hours
    E) 2 hours
    View Answer
    Option E
    Solution:
    Downstream speed = 96/8 = 12 kmph
    Speed of current = 3 kmph
    Speed of kamal in still water = 12-3 = 9 kmph
    Upstream speed = 9-3 = 6 kmph
    Time taken to cover 12 km upstream 12/6 = 2 hours

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